One mole (mol) of any substance consists of 6.022 x 10²³ molecules
(Avogadro's number). What is the translational kinetic energy of 12.00mol of
an ideal gas at 290.0K?
https://www.softschools.com/formulas/physics/kinetic_energy_of_gas_formula/337/#:~:text=In%20an%20ideal%20gas%2C%20there,or%20vibration%20within%20the%20molecules.&text=using%20the%20formula%3A-,The%20average%20translational%20kinetic%20energy%20of%20a%20single%20molecule%20of,of%20molecules%20(Avogadro's%20number).
avg kinetic energy of ideal gas is 3/2 kT. k is Boltzman constant. T is in kelvin. This give you the avg KE per molecule. Multiply that by Avogadro's number x 12.
To find the translational kinetic energy of a gas, we can use the formula:
KE = (3/2) * (n * R * T)
where:
KE is the kinetic energy
n is the number of moles of gas
R is the ideal gas constant (8.314 J/(mol*K))
T is the temperature in Kelvin
Given:
n = 12.00 mol
T = 290.0 K
Plugging in the values, we can calculate the kinetic energy:
KE = (3/2) * (12.00 mol * 8.314 J/(mol*K) * 290.0 K)
KE = (3/2) * (8.314 J/(mol*K) * 3480 J)
KE = 4.966 J/mol * 3480 J
KE = 17,246.368 J
Therefore, the translational kinetic energy of 12.00 mol of an ideal gas at 290.0 K is approximately 17,246.368 J.
To calculate the translational kinetic energy of a gas, you can use the formula:
Kinetic energy = (3/2) * N * k * T
where:
- N is the number of molecules (Avogadro's number),
- k is the Boltzmann constant (1.38 x 10^-23 J/K),
- T is the temperature in Kelvin.
In this case, we're given that there are 12.00 moles of the gas, which means the number of molecules (N) is:
N = 6.022 x 10^23 molecules/mol * 12.00 mol
Therefore, we can substitute the values into the equation:
Kinetic energy = (3/2) * (6.022 x 10^23 molecules/mol * 12.00 mol) * (1.38 x 10^-23 J/K) * (290.0 K)
By performing the calculations, you'll find the result for the translational kinetic energy of 12.00 mol of the ideal gas at 290.0 K.